Total Thrust from Soil that are Free to Move Calculator

✖Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.ⓘ Unit Weight of Soil [γ]			+10% -10%
✖Total height of wall which is under the consideration.ⓘ Total Height of Wall [h_w]			+10% -10%
✖Angle of Inclination of ground surface behind wall with horizontal.ⓘ Angle of Inclination [i]			+10% -10%
✖Angle of Internal Friction is the angle measured between the normal force and resultant force .ⓘ Angle of Internal Friction [φ]			+10% -10%

✖Total Thrust of Soil is the force acting on unit length of soil.ⓘ Total Thrust from Soil that are Free to Move [P]

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Formula

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Total Thrust from Soil that are Free to Move

Formula

P = (0.5 \cdot γ \cdot {(h w)}^{2} \cdot \cos (i)) \cdot (\frac{\cos (i) - \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}}{\cos (i) + \sqrt{{(\cos (i))}^{2} - {(\cos (φ))}^{2}}})

Example

18.89214 kN/m = (0.5 \cdot 18 kN/m³ \cdot {(3.1 m)}^{2} \cdot \cos (30 °)) \cdot (\frac{\cos (30 °) - \sqrt{{(\cos (30 °))}^{2} - {(\cos (46 °))}^{2}}}{\cos (30 °) + \sqrt{{(\cos (30 °))}^{2} - {(\cos (46 °))}^{2}}})

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Download Lateral Pressure for Cohesive and Non Cohesive Soil Formulas PDF PDF Image

Total Thrust from Soil that are Free to Move Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Thrust of Soil = (0.5*Unit Weight of Soil*(Total Height of Wall)^2*cos(Angle of Inclination))*((cos(Angle of Inclination)-sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))/(cos(Angle of Inclination)+sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2)))
P = (0.5*γ*(h_w)^2*cos(i))*((cos(i)-sqrt((cos(i))^2-(cos(φ))^2))/(cos(i)+sqrt((cos(i))^2-(cos(φ))^2)))
This formula uses 2 Functions, 5 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Total Thrust of Soil - (Measured in Newton per Meter) - Total Thrust of Soil is the force acting on unit length of soil.
Unit Weight of Soil - (Measured in Newton per Cubic Meter) - Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil.
Total Height of Wall - (Measured in Meter) - Total height of wall which is under the consideration.
Angle of Inclination - (Measured in Radian) - Angle of Inclination of ground surface behind wall with horizontal.
Angle of Internal Friction - (Measured in Radian) - Angle of Internal Friction is the angle measured between the normal force and resultant force .

STEP 1: Convert Input(s) to Base Unit

Unit Weight of Soil: 18 Kilonewton per Cubic Meter --> 18000 Newton per Cubic Meter (Check conversion here)
Total Height of Wall: 3.1 Meter --> 3.1 Meter No Conversion Required
Angle of Inclination: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Angle of Internal Friction: 46 Degree --> 0.802851455917241 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P = (0.5*γ*(h_w)^2*cos(i))*((cos(i)-sqrt((cos(i))^2-(cos(φ))^2))/(cos(i)+sqrt((cos(i))^2-(cos(φ))^2))) --> (0.5*18000*(3.1)^2*cos(0.5235987755982))*((cos(0.5235987755982)-sqrt((cos(0.5235987755982))^2-(cos(0.802851455917241))^2))/(cos(0.5235987755982)+sqrt((cos(0.5235987755982))^2-(cos(0.802851455917241))^2)))

Evaluating ... ...

P = 18892.139533535

STEP 3: Convert Result to Output's Unit

18892.139533535 Newton per Meter -->18.892139533535 Kilonewton per Meter (Check conversion here)

FINAL ANSWER

18.892139533535 ≈ 18.89214 Kilonewton per Meter <-- Total Thrust of Soil

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Geotechnical Engineering » Lateral Pressure for Cohesive and Non Cohesive Soil » Total Thrust from Soil that are Free to Move

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Created by Suraj Kumar

Birsa Institute of Technology (BIT), Sindri

Suraj Kumar has created this Calculator and 2100+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

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< Lateral Pressure for Cohesive and Non Cohesive Soil Calculators

Total Height of Wall given Total Thrust from Soil that are Free to move

Go Total Height of Wall = sqrt((2*Total Thrust of Soil)/(Unit Weight of Soil*cos(Angle of Inclination)*((cos(Angle of Inclination)-sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))/(cos(Angle of Inclination)+sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2)))))

Unit Weight of Soil given Total Thrust from Soil that are Free to Move

Go Unit Weight of Soil = (2*Total Thrust of Soil)/((Total Height of Wall)^2*cos(Angle of Inclination))*((cos(Angle of Inclination)-sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))/(cos(Angle of Inclination)+sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2)))

Total Thrust from Soil that are Free to Move

Go Total Thrust of Soil = (0.5*Unit Weight of Soil*(Total Height of Wall)^2*cos(Angle of Inclination))*((cos(Angle of Inclination)-sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))/(cos(Angle of Inclination)+sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2)))

Total Thrust from Soil when Surface behind Wall is Level

Go Total Thrust of Soil = (0.5*Unit Weight of Soil*(Total Height of Wall)^2*Coefficient of Active Pressure)

Total Thrust from Soil that are Free to Move Formula

What is Active Thrust of Soil?

The active thrust is determined from the conditions of force equilibrium and its point of application is determined from the conditions of moment equilibrium.

How to Calculate Total Thrust from Soil that are Free to Move?

Total Thrust from Soil that are Free to Move calculator uses Total Thrust of Soil = (0.5*Unit Weight of Soil*(Total Height of Wall)^2*cos(Angle of Inclination))*((cos(Angle of Inclination)-sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))/(cos(Angle of Inclination)+sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))) to calculate the Total Thrust of Soil, The Total Thrust from Soil that are Free to Move is defined as the force applied per unit length of soil. Total Thrust of Soil is denoted by P symbol.

How to calculate Total Thrust from Soil that are Free to Move using this online calculator? To use this online calculator for Total Thrust from Soil that are Free to Move, enter Unit Weight of Soil (γ), Total Height of Wall (h_w), Angle of Inclination (i) & Angle of Internal Friction (φ) and hit the calculate button. Here is how the Total Thrust from Soil that are Free to Move calculation can be explained with given input values -> 0.018892 = (0.5*18000*(3.1)^2*cos(0.5235987755982))*((cos(0.5235987755982)-sqrt((cos(0.5235987755982))^2-(cos(0.802851455917241))^2))/(cos(0.5235987755982)+sqrt((cos(0.5235987755982))^2-(cos(0.802851455917241))^2))).

FAQ

What is Total Thrust from Soil that are Free to Move?

The Total Thrust from Soil that are Free to Move is defined as the force applied per unit length of soil and is represented as P = (0.5*γ*(h_w)^2*cos(i))*((cos(i)-sqrt((cos(i))^2-(cos(φ))^2))/(cos(i)+sqrt((cos(i))^2-(cos(φ))^2))) or Total Thrust of Soil = (0.5*Unit Weight of Soil*(Total Height of Wall)^2*cos(Angle of Inclination))*((cos(Angle of Inclination)-sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))/(cos(Angle of Inclination)+sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))). Unit Weight of Soil mass is the ratio of the total weight of soil to the total volume of soil, Total height of wall which is under the consideration, Angle of Inclination of ground surface behind wall with horizontal & Angle of Internal Friction is the angle measured between the normal force and resultant force .

How to calculate Total Thrust from Soil that are Free to Move?

The Total Thrust from Soil that are Free to Move is defined as the force applied per unit length of soil is calculated using Total Thrust of Soil = (0.5*Unit Weight of Soil*(Total Height of Wall)^2*cos(Angle of Inclination))*((cos(Angle of Inclination)-sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))/(cos(Angle of Inclination)+sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))). To calculate Total Thrust from Soil that are Free to Move, you need Unit Weight of Soil (γ), Total Height of Wall (h_w), Angle of Inclination (i) & Angle of Internal Friction (φ). With our tool, you need to enter the respective value for Unit Weight of Soil, Total Height of Wall, Angle of Inclination & Angle of Internal Friction and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Total Thrust of Soil?

In this formula, Total Thrust of Soil uses Unit Weight of Soil, Total Height of Wall, Angle of Inclination & Angle of Internal Friction. We can use 3 other way(s) to calculate the same, which is/are as follows -

Total Thrust of Soil = (0.5*Unit Weight of Soil*(Total Height of Wall)^2*Coefficient of Active Pressure)
Total Thrust of Soil = (0.5*Unit Weight of Soil*(Total Height of Wall)^2*cos(Angle of Inclination))*((cos(Angle of Inclination)+sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2))/(cos(Angle of Inclination)-sqrt((cos(Angle of Inclination))^2-(cos(Angle of Internal Friction))^2)))
Total Thrust of Soil = (0.5*Unit Weight of Soil*(Total Height of Wall)^2*Coefficient of Passive Pressure)

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